Diagnostic Performance of Fractional Flow Reserve From CT Coronary Angiography With Analytical Method

The aim of this study was to evaluate a new analytical method for calculating non-invasive fractional flow reserve (FFRAM) to diagnose ischemic coronary lesions. Patients with suspected or known coronary artery disease (CAD) who underwent computed tomography coronary angiography (CTCA) and invasive coronary angiography (ICA) with FFR measurements from two sites were prospectively recruited. Obstructive CAD was defined as diameter stenosis (DS) ≥50% on CTCA or ICA. FFRAM was derived from CTCA images and anatomical features using analytical method and was compared with computational fluid dynamics (CFD)-based FFR (FFRB) and invasive ICA-based FFR. FFRAM, FFRB, and invasive FFR ≤ 0.80 defined ischemia. A total of 108 participants (mean age 60, range: 30–83 years, 75% men) with 169 stenosed coronary arteries were analyzed. The per-vessel accuracy, sensitivity, specificity, and positive predictive and negative predictive values were, respectively, 81, 75, 86, 81, and 82% for FFRAM and 87, 88, 86, 83, and 90% for FFRB. The area under the receiver operating characteristics curve for FFRAM (0.89 and 0.87) and FFRB (0.90 and 0.86) were higher than both CTCA- and ICA-derived DS (all p < 0.0001) on per-vessel and per-patient bases for discriminating ischemic lesions. The computational time for FFRAM was much shorter than FFRB (2.2 ± 0.9 min vs. 48 ± 36 min, excluding image acquisition and segmentation). FFRAM calculated from a novel and expeditious non-CFD approach possesses a comparable diagnostic performance to CFD-derived FFRB, with a significantly shorter computational time.


INTRODUCTION
Atherosclerotic plaque deposition in the coronary arterial wall results in anatomical stenosis that may reduce perfusion and induce ischemia in the subtended myocardial territory (1). Fractional flow reserve (FFR), measured during invasive coronary angiography (ICA), is the reference standard for quantifying the functional significance of coronary artery stenoses and discriminating ischemic lesions (2,3). However, ICA-based FFR measurement incurs additional resource utilization, increases procedural time, and is associated with greater patient discomfort (4). Recently, non-invasive FFR (FFR CT ) derived from computed tomography coronary angiography (CTCA) images and computational fluid dynamics (CFD) has demonstrated feasibility for the identification of ischemic coronary lesions (5) with reasonable diagnostic accuracy (6) and prognostication (7).
Mesh generation and iterative solution of numerical equations integral to CFD demand long computational time for the calculation of time-varying instantaneous values of coronary blood flow parameters like velocity, pressure, etc. The current CFD-based FFR CT methods take 1 to 4 h per FFR CT analysis (8). Reduced-order (9)(10)(11), steadyflow (12) CFD simulations and predictive models using machine learning (13)(14)(15) may improve computational efficiency and facilitate shorter turnaround times and/or on-site analysis, which will help garner a wider adoption of non-invasive FFR.
Still an analytical method to calculate FFR non-invasively without the need for computationally demanding CFD modeling would further simplify the derivation of noninvasive FFR from CTCA images. Huo et al. (16) proposed an analytical model that embodied integral equations to be solved based on the dimensions of anatomical stenosis on CTCA and estimates of hyperemic coronary flow derived from in vitro and in vivo animal experiments. In this study, we developed an original analytical method, FFR AM , that relies on neither CFD nor other inputs other than CTCA images. Flow rate through coronary lesions (Q AM ) was estimated from anatomical data reconstructed from CTCA, where anatomical features known to influence the hemodynamics in stenotic arteries, including lesion length, lumen area, flow entrance, and exit angles (17), were explicitly considered. Our aim is to assess the diagnostic performance of FFR AM with reference to our previously developed CFDbased FFR B and invasive FFR in a cohort of coronary artery disease (CAD) patients.

Study Design and Study Population
The current study consecutively enrolled patients from two tertiary centers, with age ≥ 21 years, who had undergone CTCA, and were scheduled to undergo clinically indicated ICA and FFR measurement. The time difference between CTCA and ICA was 32 (19-51) days (median, interquartile range). The exclusion criteria included prior coronary revascularization, acute coronary syndrome occurring between 30 days before CTCA and ICA, angina at rest, left ventricular ejection fraction <30%, hypertrophic cardiomyopathy, significant valve disease including prosthetic heart valve, implanted pacemaker or defibrillator, complex congenital heart disease, estimated glomerular filtration rate <30 ml/min/1.73 m 2 , tachycardia or significant arrhythmia, iodinated contrast allergy, contraindication to beta-blocker, nitroglycerin, or adenosine, serious comorbidity with life expectancy <2 years, and pregnancy. The study was approved by the local institutional review boards, and all participants gave written informed consent.
From September 20, 2016 to March 25, 2020, 117 participants were recruited. Nine subjects were excluded: two patients with unsuccessful invasive FFR measurement and seven patients with inadequate CTCA image quality. Among the seven patients, one patient had blooming artifacts due to extreme coronary calcification (Agatston score 3441), and six patients had motion artifacts in the CTCA images. By excluding 10 vessels with missing video recordings of the FFR measurement locations, 108 participants with 169 vessels were included in the analysis (Figure 1).

ICA and FFR Measurement
For the recruited patients, invasive FFR measurement was performed according to the institutional protocol. Every participant underwent ICA via either the femoral or radial approach using 5F, 6F, or 7F diagnostic or guiding catheters (18). Angiography was performed in standard projections. Diameter stenosis at ICA (DS ICA ) was visually assessed (19), and lesions were deemed obstructive if DS ICA ≥50%. The pressure wires/catheters used for the invasive FFR can be found in the Supplementary Material. Intra-coronary pressure was measured at the ascending aorta and distal to the coronary lesion in at least one vessel. Hyperemia was induced by either intravenous infusion (140-180 µg/kg/min) or an intracoronary bolus (60-200 µg) of adenosine. A coronary lesion was categorized as ischemic if FFR ≤0.80. Two consultant interventional cardiologists with extensive clinical experience reviewed the ICA images, and the lesions were evaluated based on overall consensus. In case of disagreement, a third independent cardiologist reviewed the films and provided a final diagnosis.

CTCA Acquisition
Every participant underwent CTCA on one of the following scanners with ≥256 detector rows: Toshiba Aquilion One 320 Slice, Canon Aquilion ONE Genesis 640 Slice, Philips Brilliance iCT 256-detector, Siemens Somatom Force dual source 384detector, GE Revolution single source, and Siemens Somatom Drive dual source 256-detector. Oral beta-blocker (metoprolol) was administered to the participants with a heart rate >65 beats per min (20). Sublingual glyceryl trinitrate was administered just prior to scanning for optimal coronary vasodilation during image acquisition. Prospective electrocardiogram-triggered protocol was used to acquire image data at pre-specified phases of the heart cycle, and CTCA scan was performed at inspiratory breathhold. Then, 50 to 75 ml of non-ionic contrast Omnipaque 350 was administered for each scan.

CTCA Image Segmentation and 3D Model Reconstruction
Dedicated QAngio CT software (21) (version 3.0, Medis) was used for segmentation and 3D reconstruction of coronary artery. Additional details are found in the Supplementary Material. The surface meshes of the 3D coronary artery tree model were generated using 3D Workbench (version 0.8, Medis). Figure 2 illustrates the workflow for non-invasive FFR calculation in a participant. Figure 3 depicts the detailed coronary anatomy in another participant with pertinent anatomical parameter inputs for calculating the FFR AM .
Total coronary flow under resting conditions, a required input parameter for non-invasive FFR estimation, is linearly related to left ventricular mass (LVM) (22). The latter was measured using validated Segment CT software (version 2.2, Medviso) (23) that semi-automatically delineated left ventricular (LV) endocardial and epicardial contours on contiguous 2D LV shortaxis slices reformatted from the CTCA-reconstructed 3D wholeheart model (Figure 3).

Computation of Non-invasive FFR AM With Analytical Model
In our analytical model, FFR AM = 1− P 1 +P 2 P a , where P a is patientspecific mean aortic pressure estimated as mean cuff pressure minus 6.8 mmHg to account for pressure drop during hyperemia (24), and P 1 and P 2 are pressure drops across the coronary lesion and from the coronary orifice to the proximal end of the coronary lesion, respectively. The latter is calculated from the Hagen-Poiseuille equation according to the viscosity of the blood, lumen area, length, and flow rate of each coronary branch (from the coronary orifice to the proximal end of the coronary lesion), respectively. By law of energy conservation, P 1 entails convective and diffusive energy losses as well as energy loss attributable to sudden constriction and expansion (16). Flow separation and swirling that exacerbate energy losses and pressure drops are related to features such as lesion length, lumen area, flow entrance, exit angles, etc. (25). We applied these considerations in series to a coronary lesion model of total length L decomposed schematically into three components: a proximal contracting segment of length L ps and distal expanding segment of length L sd , which bookend a middle maximally stenosed segment of finite length L-L ps -L sd (Supplementary Figure 1). The respective pressure drops across the three segments P ps , P sd , and P ss sum up to P 1 and are, from a mechanical engineering perspective, analogous to pressure drops across contracting, expanding, and straight pipes, respectively (Supplementary Material). Figure 3F illustrates how we measured the anatomical parameters L, L ps , and L sd as well as A P , A d , and A s , the lumen areas at the proximal and distal ends of the coronary lesion, and the maximally stenosed segment, respectively. From these parameters, flow entrance (α) and exit (β) angles were derived to facilitate the calculation of P ps and P sd (Supplementary Material).
To calculate the hyperemic flow rate of each coronary branch, we first calculated the total coronary flow rate at resting from CTCA-assessed LVM (22) and then estimated the resting flow rate through the i-th coronary branch using the scaling law (26). Finally, hyperemic flow rate through a coronary lesion located at the i-th branch of the coronary artery tree was computed as k times of its value at resting state . (24). The coefficient k reflects the magnitude of flow increase at hyperemia and is dependent on the diameter stenosis of the lesion (DS). Inputting Q AM to the analytical model, P 1 and then FFR AM could be calculated without a need for CFD simulation (Supplementary Material).

Computation of Non-invasive FFR B Based on Reduced-Order CFD Simulation
Reduced-order CFD simulation was performed on the reconstructed 3D coronary artery tree model in deriving noninvasive FFR B measurement. Additional details can be found in our prior studies (9,11,27) and in the Supplementary Material. The FFR B value was extracted at the location on the 3D coronary tree model that best corresponded to the site of the FFR measurement at ICA as judged by cardiologists (JMF and CYC).

Statistical Analysis
Continuous variables were summarized as mean ± standard deviation (SD) or median (interquartile range), and the categorical variables were summarized as frequencies and percentages. Two-sample t-test, Wilcoxon rank-sum test, and Fisher's exact test were used to compare the ischemic and nonischemic groups on continuous normally distributed variables, continuous parameters with non-normal distribution, and binary variables, respectively. For vessels with multiple lesions, the pressure drops over individual lesions were compared, and the anatomical parameters associated with the lesion contributing to the largest pressure drop were selected for statistical analysis. The DeLong test (28) was used to compare receiver operating characteristic (ROC) areas under the curve (AUCs). Accuracy, sensitivity, specificity, positive prediction value, negative predictive value (NPV), and likelihood ratios corresponding to the diagnostic threshold were calculated to enable a comparison of the discrimination capability among DS CTCA , DS ICA , and non-invasive FFR indexes. SPSS (version 22, IBM, New York, USA) was used to perform the statistical analyses. Statistical significance was set at p <0.05.

Characteristics of Flow Rate and Morphological Parameters
Among 169 vessels, 73 (43%) were ischemic ( Table 2). A s and A d were significantly smaller, and α and β were significantly greater among ischemic vs. non-ischemic lesions, which contribute to the significantly greater P ps and P sd along the contracting and expanding segments, respectively, in the ischemic lesions. There was excellent correlation between flow rates through lesions derived using empirical equations and CFD simulation (mean Q AM 3.38 ± 1.93 ml/s vs. mean Q CFD 3.30 ± 1.97 ml/s; r = 0.95, p < 0.0001) (Figure 4).  and agreement with small systematic biases (-0.0027 ± 0.163) (Figure 4). Performance metrics using DS CTCA ≥50%, DS ICA ≥50%, FFR AM ≤0.8, and FFR B ≤0.8 to discriminate ischemic lesions are compared in Table 3 and Figure 5.

Computational Time FFR AM vs. FFR B
Excluding image acquisition and segmentation, the computational time for FFR B was 48 ± 36 min (range 0.12 to 3.67 h) using parallel computation on a Dell T7800 workstation. The corresponding computational time for FFR AM was 2.2 ± 0.9 min, using a single CPU of the same workstation.

DISCUSSION
In this study, we have developed a novel analytical method to determine FFR AM non-invasively from patient-specific 3D models reconstructed from CTCA images. The FFR AM exhibited a good correlation with invasive FFR and had a diagnostic performance close to CFD-based FFR B . We have also demonstrated the diagnostic performance of FFR B in a prospective study design. The computational time for FFR AM was much shorter than that for FFR B .
Our analytical model compartmentalized the stenosed coronary vessel into segments with distinct geometry to simplify the calculation of the corresponding pressure drops. We used anatomical information and LVM to calculate the flow rate through lesions and then input them into empirical equations with anatomical parameters measured on 3D coronary models to calculate energy loss due to the expansion and constriction of the lumen cross-section, which facilitates non-invasive FFR AM calculation. A major advantage of estimating FFR AM non-invasively using the analytical model is computational speed since the computational cost of CFD is eliminated. The analysis took slightly more than 2 min on a single CPU. This speed was achieved with little compromise in diagnostic accuracy. The flow rates through the lesions calculated in our analytical method using only anatomical information had a good correlation with that obtained by CFD simulation (r = 0.95), and the derived FFR AM demonstrated a fair correlation and good agreement with invasive FFR and was close to FFR B . For the diagnosis of ischemia, FFR AM had similar AUC (0.89 vs. 0.90, p = 0.57 and 0.87 vs. 0.86, p = 0.78 on per-vessel and per-patient bases, respectively) and specificity (86 vs. 86% and 79 vs. 77% on per-vessel and per-patient bases, respectively) but with slightly lower sensitivity (75 vs. 88% and 73 vs. 86% on per-vessel and per-patient bases, respectively) and NPV (82 vs. 90% and 70 vs. 82% on per-vessel and per-patient bases, respectively) compared with FFR B . Notably, both methods had superior diagnostic performance to routine methods, including DS CTCA and DS ICA . The FFR AM derived from the lesion lumen area, length, flow entry and exit angles, and flow rate with fluid equations is different from diameter stenosis and other measurements of coronary morphologic information. It is related more to coronary hemodynamics and physiology. The lesion length and diameter have been employed by other investigators as indirect measures of fractional flow reserve (29). Our current study showed a greater mean value of lesion length (11.46 ± 7.40 vs. 10.07 ± 5.97 mm, p = 0.223) and a smaller lesion area (3.05 ± 1.56 vs. 4.56 ± 2.41 mm 2 , p < 0.0001) in the group with FFR ≤0.8 vs. the group with FFR >0.8. As a result, the estimated coronary morphologic index [eg., lesion length/minimal lesion diameter (29)] from our study is significant greater (12.3 vs. 4.8, p < 0.0001) in the group with FFR ≤0.8 vs. the group with FFR >0.8, which is in agreement with the findings from the study of Li (29). In addition to the aforementioned coronary morphologic index, other lesion geometric parameters, like flow entry and exit angles to lesions, have been associated with fluid convective and diffusive energy loss and pressure drop (3,4). We have incorporated these additional elements in formulating the expressions for FFR AM calculation. By decomposing a coronary lesion model of finite length into a spatial series of a proximal contracting segment, middle stenotic segment, and distal expanding segment to derive the model equations, FFR AM presents an integrated assessment of coronary hemodynamics that provides a more accurate assessment of coronary physiology than morphologic stenosis index.
While CFD-based non-invasive FFR can improve the diagnostic performance of DS CTCA alone, it is provided as a remote service with a long turnaround time due to the significant computational costs incurred for mesh generation and iterative solutions to solve numerical equations, which are procedures intrinsic to flow simulation (5,6). To facilitate on-site noninvasive FFR computation, Coenen et al. (31) modeled the coronary vessel as a 1D segment for simulation and mapped the calculated cFFR onto the 3D model reconstructed from CTCA images. The computational time was reduced to 5-10 min per patient, but the accuracy was only 74.6% with invasive FFR as reference (31). Machine-learning based artificial intelligence (AI) algorithms were introduced to reduce the calculation time of non-invasive FFR in some studies that were mainly based on retrospective investigations (13)(14)(15). These required ample synthetic datasets for training before the AI algorithms could be applied. Another option to reduce computational time entails the use of analytical models. Huo et al. (16) reported an analytical method to estimate FFR from the dimensions of stenosis and hyperemic coronary flow. The method relied on in vitro or animal experiments to obtain hyperemic coronary flow, which hindered its applicability outside the laboratory. In contrast, our new analytical model uses only anatomical information and does not require in vitro or in vivo experiments. With relatively similar diagnostic performance as and lower computational demand than CFD-based approaches, the application of FFR AM for onsite non-invasive FFR analysis may become feasible.

Linkage of Parameters in the Analytical Model to Features in AI Algorithms
AI algorithms can facilitate non-invasive FFR estimation (13). The judicious selection of input parameters plays an important role in the accuracy of machine learning. Table 2 shows the list of anatomical features measured on or derived from CTCAderived 3D coronary models and their discriminative capability for ischemic lesions. These parameters can aid in the feature selection of diagnostic AI algorithms. Flow quantitation by machine learning can also be facilitated using anatomical features since the coronary flow rates in the lesions that were derived from anatomical information showed a strong correlation with the CFD simulation results in our study (r = 0.95, p < 0.0001).
Minimal lumen area measured on intravascular ultrasound has been correlated with FFR-ascertained ischemia (32), and a minimal lumen area ≤3.0 mm (2) indicates a high likelihood of significant obstruction in a normal-sized coronary vessel (32). Accordingly, minimal lumen area has been adopted as one of the features for angiography-based machine learning algorithms (33). In our study, the lumen area at the site of maximum stenosis (A s ) was significant smaller in ischemic vs. non-ischemic lesions (3.05 ± 1.56 vs. 4.56 ± 2.41 mm 2 , p < 0.0001), and we believe that it is a prime candidate for feature selection in machine learning. Due to curvature changes in the stenotic region, the flow entrance and exit angles α and β were significantly different between the ischemic and non-ischemic lesions in this study. As such, their effects on FFR prediction can be explored in future machine learning, together with other anatomical parameters, such as lumen areas, lesion lengths, etc.
Despite the potential of AI to non-invasive FFR, its clinical application remains challenging. The problem in AI lies in training data paucity, clinical interpretation, commercial deployment, and safety. Our method is based on coronary morphologic parameters and fluid dynamic principles and does not need training data. Importantly, the calculation can be completed with a much shorter computational time than full computational fluid dynamics. Lastly, we have developed a visualization system for physicians to view the computational results from both anatomic modeling and calculated FFR AM and FFR B . This holds a potential application for the further personalized management of CAD patients like virtual stent simulation in our recent publication (34).

Limitations of the Study
There are limitations in this study. First, a high calcium score may preclude accurate segmentation, which is a problem common to all CTCA-based analysis. The lumen segmentations were carefully examined by two experienced radiologists in the current study to ensure the accuracy of the results. Second, hyperemia was induced by either an intravenous infusion or intracoronary bolus of adenosine; nonetheless, prior studies have reported that the intravenous infusion of adenosine yielded an identical FFR result compared with intracoronary bolus (35). Lastly, this study did not use recently developed instantaneous wave-free ratio and resting full-cycle ratio non-hyperemic indexes of coronary artery stenosis severity as a reference method.

CONCLUSIONS
In this prospective multicenter study, an analytical method that calculates non-invasive FFR AM from CTCA and anatomical features offers a novel and expeditious non-CFD approach that demonstrated good diagnostic performance for detecting ischemic coronary lesions as ascertained by invasive FFR.

DATA AVAILABILITY STATEMENT
The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding authors.

ETHICS STATEMENT
The studies involving human participants were reviewed and approved by SingHealth Centralised Institutional Review Board. The patients/participants provided their written informed consent to participate in this study.